Some insects are living in my children’s sand pit. I don’t know what they are and I don’t know where they are, but without question they are in there. If the sand pit has not been used for a few days the surface of the sand is covered by small tracks. The movement of the insects smooths the larger hills and castles, and the visual effect of the trails, give or take considerations of colour, is ...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness...

The complex dynamical analysis of the cubic-order iterative family is made to draw the fractal images by means of Möbius conjugacy map applied to a prototype polynomial of the form (z − A) (z − B) . The related dynamics is best displayed through various stability surfaces and parameter spaces.

The analysis of the distribution of stars in open clusters may yield important information on the star formation process and early dynamical evolution of stellar clusters. Here we address this issue by systematically characterizing the internal spatial structure of 16 open clusters in the Milky Way spanning a wide range of ages. Cluster stars have been selected from a membership probability ana...

many studies suggested that fractals could be brought in any structural anarchy, such as cancers, for diagnosis and prognosis evaluation by quantifying it and expressing it in terms of fractal geometry. in this study, we aimed to evaluate pathologic grades or breast carcinomas by fractal analysis. this cross-sectional study was performed on 60 women with breast ductal carcinoma. from all the pa...

We prove that the Farey sequences can be express into equivalence classes labeled by a fractal parameter which looks like a Hausdorff dimension h defined within the interval 1 < h < 2. The classes h satisfy the same properties of the Farey series and for each value of h there exists an algebraic equation. PACS numbers: 02.10.Lh, 02.30.Lt

M. F. Barnsley proposed the concept of fractal interpolation function (FIF) using iterated function systems (IFS) to describe the real world objects. The purpose of this paper is to study the parameter identification method for FIF with vertical scaling factor functions (VSFF) for one dimensional data set and establish the generalized version of the analytic approach of Mazel [13].

In this paper the authors describe the results of experiments for surface roughness image acquisition and processing in order to develop an automated roughness control system. This implies the finding of a characteristic roughness parameter (for example Ra) on the bases of information contained in the image of the surface. To achieve this goal we use quasi-fractal characteristics and fuzzy clus...

This paper presents some interesting results of numerical analysis of the Extended Blaschke functions, which are constructed by extending Blaschke product. On the complex plane, the convergent domains of the functions form fractal patterns of constrained Herman rings with limited-layered structures, which demonstrate skip-symmetry, symmetry broken, chaos, and degeneracy in conjunction with para...